Physicists Simulate Cosmic Geometries to Study Spacetime Dimensions

A trio of physicists from the University of Belgrade, in Serbia, has released a preprint paper on arXiv proposing a mathematical theory regarding the dimensions of the universe. The research, which has not yet been peer-reviewed, uses a toy model of quantum gravity to simulate different cosmic geometries using virtual four-dimensional triangles, known as 4-simplices.

Simulation Methodology

The researchers modeled a miniature universe that decreases from four to zero dimensions. The structure begins with four-dimensional 4-simplices, which are composed of three-dimensional tetrahedra, two-dimensional triangles, one-dimensional edges, and zero-dimensional vertices.

Key aspects of the simulation included:

• Edge Lengths: Researchers randomized edge lengths, setting the minimum at the Planck length (10⁻³⁵ meters).
• Topologies: The study tested three configurations using approximately 100,000 simplices: a four-dimensional ball with a boundary, a four-dimensional sphere without a boundary, and a disconnected set of simplices used as a control.
• Edge Types: Edges were treated as space-like (represented by real numbers), time-like (represented by imaginary numbers), or a combination of both.

The final data pool consisted of over 20 billion evaluations of these simulations.

Simulation Results

According to the researchers, the simulations yielded several different spacetime signatures:

• Three Spatial, One Temporal: Up to about 85 percent of the trials organized into a spacetime with three spatial dimensions and one temporal dimension.
• Euclidean Signature: Around 6 percent of trials resulted in a "frozen Universe" with four spatial dimensions and no time.
• Split Universe: Approximately 8 percent of trials yielded a universe with two dimensions of space and two dimensions of time, though this occurred only when edge lengths were treated as space-like.

When edges were treated as time-like or a mixture, the results yielded signatures with two or even three dimensions of time.

Findings on Topology and Edges

The study found that the global topology—whether the universe was a ball, sphere, or a jumble of pieces—made little difference to the outcome. The researchers noted that this suggests the split between space and time might be set locally, or that topological differences average out with enough pieces.

Additionally, the researchers found that space-like edges alone were sufficient to produce a time direction, as edges of mismatched lengths often only fit together in a geometry that includes a time direction.

Why it matters

This research seeks to test "whether the spacetime signature can ultimately be understood as an emergent property of quantum geometry," the researchers conclude. Future research may include various shapes and physical laws to further test the model.

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Sources

• yahoo.com: A Strange New Theory Helps Explain Why Our Universe Has Only One Dimension of Time
• sciencealert.com: A Strange New Theory Helps Explain Why Our Universe Has Only One Dimension of Time : ScienceAlert

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